This document discusses the drift flux model (DFM), which is a separated flow model that focuses on the relative motion of phases rather than individual phase motion. The key assumption of DFM is that the dynamics of two phases can be expressed by the mixture momentum equation. DFM modifies mixture properties from homogeneous equilibrium model by correction factors. It provides equations for drift flux, mixture properties like density and phase velocities, and is applicable to various two-phase flows. However, it is not suitable for acoustic waves, choking phenomena, or high frequency instabilities.

1. Drift Flux Model
By: Yadav Gaurav N
M.Tech Thermal Sciences
Project Guide:
Dr. S.Jayaraj

2. Introduction
• DFM is essentially a seperated flow model in which
attention is focused on the relative motion rather than the
motion of the individual phase motion.
• Important assumption associated with the DFM is that the
dynamics of two phases can be expressed by the mixture
momentum equation.
• It modifies all the mixture properties of HEM by suitable
correction factor.

3. Drift Flux.
• j21 : Drift flux of component 2 wrt component 1.
j21 = α(u2-jTP)
• Physically it is velocity of one fluid wrt to a observer
moving at average velocity.
j21 = -j12

4. Mixture Properties
• j21 = α(u2 - j) = α(u2 – j1 –j2)
= α((j2/ α) – j1 –j2)
j21 = j2 – αj.
• Thus αDF = (j2 – j21)/j.
• For HEM, α = j2/(j1+j2)

5. • So , αDF = (j2 – j21)/j.
= (j2/j)*(1-(j21/j) )
= (j2/j1+j2)*(1-(j21/j) )
= αHEM * ((1-(j21/j) )).
• Therefore,
αDF = αHEM * Correction Factor.

6. • Mixture Density:
ρTP= α* ρ2 + (1- α) ρ1.
ρHEM = {(j2/j)* ρ2 + (j1/j)* ρ1}
ρDFM = {(j2 - j21)/j}* ρ2 + {(j1 + j21)/j}* ρ1.
= {(j2/j)* ρ2 + (j1/j)* ρ1} + (j21/j)*(ρ1 – ρ2).
Therefore,
ρDFM = ρHEM + Correction Factor

7. • Phase Velocities :
u1 = j1/(1-α) = (j1*j)/(j1 + j21)
= j/{1 + (j21/j1)}.
• For HEM, u1 = u2 = j1 = j2 =j i.e. the two
phases move at same velocities as no slip is
present between the phases.
• u1DFM= j/(Correction Factor).
• Same case holds true for u2DFM

8. Merits & Demerits.
• Simplicity.
• Applicable to a wide range of two phase flows like:
Bubbly.
ii. Slug
iii. Droplet
iv. Annular
v. Fluidized Bed.
i.
•
i.
ii.
iii.
Not suitable for:
Acoustic wave propagation.
Choking Phenomena
High frequency instabilities.

9. •
Drift Flux Model has four equations :
1.
2.
3.
4.
Mixture Continuity.
Mixture Momentum.
Mixture Energy.
Gas Continuity.

10. Approach to estimate j21 by kinematic
constitutive equation
• There are two ways :
1. Concentrate mixture as a whole and apply the laws to
them rather than individual phases.
2. Two fluid formulation.
• Generally two fluids are not in thermal equilibrium. So we
cannot define Tmix and other mixture properties.
• Whether the dispersed flow exhibits bubbly, churn , slug
etc influence the constitutive laws. But the type of flow
changes continuously. So the laws to be applied also
changes.

11. Two Fluid Formulation.
• Momentum Equation:
u1
t
u1
u1
b1
u
t
u2
u2
b2
f
f
1
2
p
p
f’s are the left over forces which have to be incorporated to
keep the account straight.

12. • For Newtonian fluid incompressible one component and no
phase change :
f1
•
1.
2.
3.
4.
2
1
Generally f’s arise from:
Wall shear stress.
Particle particle interaction.
Hydrodynamic drag.
Forces during momentum changes during evaporation and
condensation.

13. • For steady state 1-D conditions:
0
0
1
g
2
g
dp
dz
dp
dz
F1
1
F2
Per unit volume of phase 1 and 2 respectively.
F1 = f1(1-α) and F2 = f2 α

14. Forces acting on fluid 1 and 2 other than
pressure gradient.
•
Fw = Force arising from the wall.
• F12 = Due to interaction between the two fluids.
•
velocity of phase 2 is greater than phase 1

15. • f1 = Force per unit volume of phase 1.
• f2 = Force per unit volume of phase 2.
• f1(1-α) = F1 = Force per unit volume of total flow field.
• f2(1- α) = F2 = Force per unit volume of total flow field.
• F1 = F12 – Fw1
• F2 = -F12 – Fw2

16. • Finally on simplification the momentum equations become
0
1
0
dp
dz
g
2
dp
dz
g
F 12
1
F 12
• Subtracting the two equations,
0
F 12
2
1
g
F 12
1
F 12
g

17. • The previous equation is obtained in the situation where
only hydrodynamic drag is important i.e. the wall shear
stress is neglected.
• F12 = F12(component properties, void fraction, interface
geometry, relative motion).
• For a given system, ρ is constant.
• F12 = F12(α , j21) only.
•
For a given system j21 = j21(α) only.

18. • After series of experiments scientist found that
j21 = j21(α , u∞)
where u∞ is the velocity of one discontinuous particle of phase
2 in the infinite medium of phase 1.
Thus ,
j21 = u∞ α(1- α)n .
• The other equation obtained previously was
j21 = j2 – αj
The solution is thus obtained graphically.